MinT - Best Known (87−26, 87, s)-Nets in Base 4

Best Known (87−26, 87, s)-Nets in Base 4

(87−26, 87, 312)-Net over F₄ — Constructive and digital

Digital (61, 87, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 29, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(87−26, 87, 435)-Net over F₄ — Digital

Digital (61, 87, 435)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−26, 87, 20194)-Net in Base 4 — Upper bound on s

There is no (61, 87, 20195)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23952 655742 848641 766989 347049 824236 476759 416825 436400 > 4⁸⁷ [i]